Midterm Solutions 2007

Midterm Solutions 2007 - s I t'hto S $'i*J nr I SJ'hu'r 9cl...

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I t'hto s nr I SJ'hu''r 9cl rl L czo-l ; S $'i*J { C1h,.tcr ildh'Pt f .u^ " f"tr" tft *ro. orroJ c.^, Tcrl-c- + tu1 =tul$ *T * 5<a Aevl +1.n (o.j',t t^, E= Lutt .Tr"Z.1- T 7 *vt a- ( "lu'.-^ F"tih'-) l?-f = I* l;F ..!jl c4 lC /V1q .rltacl e - | - ttfrt Lr?- f, truD c h n F hdL,L l : (-rL fix4l- ro.J ,-,F. cr,rr1J,r ,-h b.J- e^t "{ tt -* e'- {^" t* L'frp'|,,on- h,?^^a-=t.ryF,?-s ? d_t Yl I-1 '^ - It.lA. .l-z .. A!a* c0^ rti' | ! f Iru {=mto. :. AJ +ut1 . .F tpC^J go;,^f 72' r + h,rnr,-=u^1 + ct-zftl J"lt\ , Vg'- ur' -- Lax UI =G3 t.)t' Lo. .^." U q*ntt- L &Jl^A" =) I= ,*tTT(;rC') \-/ | v I I l" a '1 4 il,J D lrh,. +l*tU sg.r^I a\ {rt.,h'o^^( Lur* o,*t ,-JA $rn yN It ,..,l t 't e" Lrie{ k-- h't A?": fntlU =A4=fr =)Vx=# dtr---rY*-'Tvr J" ry (ro' L^^ (tt\*trA.s) 5c ) = ,!. 3 1 + /x=@ lv ou
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Problem 2a. The disk has mass M, ffi to avoid confusion, let the rocket have mass rn(t) such that m(0) - M. We take the fuel speed u with respect to the rocket to be a positive quantity (unlike K&K). The moment of inertia of the disk and rocket system about the post is 1 1(r) ;r*'+m(t)R2 . At a time t, the disk and rocket have angular momentum L(t) /(t)c. .'(t). To be consistent with the diagram, the angular momentum points out of the page.
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Midterm Solutions 2007 - s I t'hto S $'i*J nr I SJ'hu'r 9cl...

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